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Polytropic Efficiency

The isentropic efficiency has one significant drawback in that there is no way to separate the fluid dynamic losses from the total (fluid dynamic + thermodynamic) losses. This means that devices having different pressure ratios will have different isentropic efficiencies even though they may both be of similar fluid dynamic quality. An example would be two compressors of different pressure ratios. The higher pressure ratio compressor will have a lower isentropic efficiency because of thermodynamic losses. This property can make it difficult to comparatively evaluate different compressor designs. A similar argument applies to turbine design.

To work around this drawback, the assumed "ideal" path followed by the process does not have to be an isentrope. Instead, one can evaluate the polytropic efficiency by following a path along a line of constant efficiency. Aungier [65] discusses how a constant efficiency path on a T-s diagram can be approximated by the following equation:

Equation 32.      

This equation can be rearranged to give the following two relationships:

Equation 33.      

The entropy change along this path is evaluated by integrating the last expression:

Equation 34.      

Rearranging this expression gives the value of the constant along the given path:

Equation 35.      

In order to evaluate the polytropic efficiency, evaluate the polytropic enthalpy change along the alternative path defined by the path equation. First, start with the second law:

Equation 36.      

The term is the polytropic work, or enthalpy change, and is what needs to be solved. First, the term is substituted using Equation 33 to give:

Equation 37.      

Integrating this equation along the polytropic path gives:

Equation 38.      

Note

The term has been renamed to to signify that the work is the polytropic enthalpy change.

The final form of the polytropic work is obtained by simply substituting for :

Equation 39.      

Now that you have an expression for this enthalpy change, you can compute the polytropic efficiency:

Equation 40.      

The polytropic efficiencies are also evaluated relative to a selected inlet boundary condition and output by the flow solver as both local (at every node in the flow) and global (overall device) quantities.